Question: Simplify the following expression: $k = \dfrac{-9x^2 + 117x - 270}{x - 10} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-9$ , so we can rewrite the expression: $ k =\dfrac{-9(x^2 - 13x + 30)}{x - 10} $ Then we factor the remaining polynomial: $x^2 {-13}x + {30} $ ${-10} {-3} = {-13}$ ${-10} \times {-3} = {30}$ $ (x {-10}) (x {-3}) $ This gives us a factored expression: $\dfrac{-9(x {-10}) (x {-3})}{x - 10}$ We can divide the numerator and denominator by $(x + 10)$ on condition that $x \neq 10$ Therefore $k = -9(x - 3); x \neq 10$